The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

1.
A.
Gérard
, “
Tara y tarka. Un sonido, un instrumento y dos causas (Estudio organológico y acústico de la tarka)
,” en
Diablos tentadores y pinkillus embriagadores en la fiesta de Anata/Phujllay. Estudios de antropología musical del carnaval en los Andes de Bolivia
, edited by
A.
Gérard
(
Plural editores
,
La Paz
,
2010
), Vol.
1
, pp.
69
140
.
2.
H.
Stobart
, “
Tara and Q'iwa - Worlds of Sounds and Meaning
,” in
Cosmología y Música en los Andes
, edited by
M. P.
Baumann
(
International Institute for Traditional Music
,
Vervuert Iberoamericana, Berlin
,
1996
), pp.
67
81
.
3.
H.
Stobart
,
Music and the Poetics of Production in the Bolivian Andes
(
SOAS Musicology Series-Ashgate
,
United Kingdom
,
2006
).
4.
D.
Keefe
and
B.
Laden
, “
Correlation dimension of Woodwind multiphonic tones
,”
J. Acoust. Soc. Am.
90
,
1754
1795
(
1991
).
5.
C.
Maganza
,
R.
Caussé
, and
F.
Laloë
, “
Bifurcation, period doubling and chaos in clarinet like systems
,”
Europhys. Lett.
1
,
295
302
(
1986
).
6.
N. H.
Fletcher
, “
Mode locking in nonlinearly excited inharmonic musical oscillators
,”
J. Acoust. Soc. Am.
64
,
1566
1569
(
1978
).
7.
T. D.
Wilson
and
D. H.
Keefe
, “
Characterizing the clarinet tone: Measurements of Lyapunov exponents, correlation, dimension and unsteadiness
,”
J. Acoust. Soc. Am.
104
,
550
561
(
1998
).
8.
W.
Lauterborn
and
U.
Parlitz
, “
Methods of chaos physics and their application to acoustics
,”
J. Acoust. Soc. Am.
84
,
1975
1993
(
1988
).
9.
M.
Castellengo
,
Sons Multiphoniques aux Instruments a Vent
(
Rapports IRCAM Nr. 34/82
,
Paris
,
1982
).
10.
E.
Leipp
,
Acoustique et Musique
(
Masson
,
Paris
,
1976
).
11.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
(
Cambridge University Press
,
Cambridge
,
2003
).
12.
F.
Takens
, “
Detecting strange attractors in fluid turbulence
,” in
Dynamical Systems and Turbulence
, edited by
D.
Rand
and
L. S.
Young
(
Springer
,
Berlin
,
1981
), pp.
366
381
.
13.
T.
Sauer
,
J. A.
Yorke
, and
M.
Casdagli
, “
Embedology
,”
J. Stat. Phys.
65
,
579
616
(
1991
).
14.
R.
Hegger
,
H.
Kantz
, and
T.
Schreiber
, “
Practical implementation of nonlinear time series methods: The TISEAN package
,”
Chaos
9
,
413
435
(
1999
).
15.
J. A.
Armstrong
,
N.
Bloembergen
,
J.
Ducuing
, and
P. S.
Pershan
, “
Interactions between light waves in a nonlinear dielectric
,”
Phys. Rev.
127
,
1918
1939
(
1962
).
16.
A. H.
Nayfeh
and
D. T.
Mook
,
Nonlinear Oscillations
(
John Wiley & Sons, Inc.
,
New York
,
1995
).
17.
N. H.
Fletcher
, “
Acoustical correlates of flute performance technique
,”
J. Acoust. Soc. Am.
57
,
233
237
(
1975
).
18.
F. M.
Atay
, “
Total and partial amplitude death in networks of diffusively coupled oscillators
,”
Physica D
183
,
1
18
(
2003
).
19.
D. V.
Ramana Reddy
,
A.
Sen
, and
G. L.
Johnston
, “
Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators
,”
Phys. Rev. Lett.
85
,
3381
3384
(
2000
).
20.
A.
Stefanski
and
T.
Kapitaniak
, “
Steady state locking in coupled chaotic systems
,”
Phys. Lett. A
210
,
279
282
(
1996
).
21.
W.
Zou
,
D. V.
Senthilkumar
,
J.
Duan
, and
J.
Kurths
, “
Emergence of amplitude and oscillation death in identical coupled oscillators
,”
Phys. Rev. E
90
,
032906
(
2014
).
22.
T.
Banerjee
and
D.
Biswas
, “
Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion
,”
Chaos
23
,
043101
(
2013
).
23.
A.
Koseska
,
E.
Volkov
, and
J.
Kurths
, “
Oscillation quenching mechanisms: Amplitude vs. oscillation death
,”
Phys. Rep.
531
,
173
199
(
2013
).
24.
A.
Koseska
,
E.
Volkov
, and
J.
Kurths
, “
Transition from amplitude to oscillation death via Turing bifurcation
,”
Phys. Rev. Lett.
111
,
024103
(
2013
).
25.
G.
Gottwald
and
I.
Melbourne
, “
On the implementation of the 0–1 test for chaos
,”
SIAM J. Appl. Dyn. Syst.
8
,
129
145
(
2009
).
26.
J.
Guckenheimer
and
P.
Holmes
,
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
(
Springer
,
New York
,
1986
).
27.
E.
Ott
,
Chaos in Dyamical Systems
(
Cambridge University Press
,
Cambridge
,
2002
).
28.
H. D. I.
Abarbanel
,
Analysis of Observed Chaotic Data
(
Springer
,
New York
,
1996
).
29.
H.
Kantz
,
G.
Radons
, and
H.
Yang
, “
The problem of spurious Lyapunov exponents in time series analysis and its solution by covariant Lyapunov vectors
,”
J. Phys. A: Math. Gen.
46
,
254009
(
2013
).
30.
S.
Giannerini
and
R.
Rosa
, “
New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation
,”
Physica D
155
,
101
111
(
2001
).
31.
S.
Giannerini
,
R.
Rosa
, and
D. L.
Gonzalez
, “
Testing chaotic dynamics in systems with two positive Lyapunov exponents: a bootstrap solution
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
17
,
169
182
(
2007
).
32.
N.
Marwan
,
M.
Romano
,
M.
Thiel
, and
J.
Kurths
, “
Recurrence plots for the analysis of complex systems
,”
Phys. Rep.
438
,
237
329
(
2007
).
33.
E. J.
Ngamga
,
A.
Buscarino
,
M.
Frasca
,
G.
Sciuto
,
J.
Kurths
, and
L.
Fortuna
, “
Recurrence-based detection of the hyperchaos-chaos transition in an electronic circuit
,”
Chaos
20
,
043115
(
2010
).
34.
O. A.
Rosso
,
H. A.
Larrondo
,
M. T.
Martin
,
A.
Plastino
, and
M. A.
Fuentes
, “
Distinguishing noise from chaos
,”
Phys. Rev. Lett.
99
,
154102
(
2007
).
35.
F.
Olivares
,
A.
Plastino
, and
O. A.
Rosso
, “
Contrasting chaos with noise via local versus global information quantifiers
,”
Phys. Lett. A
376
,
1577
1583
(
2012
).
36.
M.
Sano
and
Y.
Sawada
, “
Measurement of the Lyapunov spectrum from a chaotic time series
,”
Phys. Rev. Lett.
55
,
1082
1085
(
1985
).
37.
T.
Kapitaniak
and
L. O.
Chua
, “
Hyperchaotic attractors of unidirectionally-coupled Chua's circuits
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
4
,
477
482
(
1994
).
38.
T.
Kapitaniak
,
L. O.
Chua
, and
G. Q.
Zhong
, “
Experimental hyperchaos in coupled Chua's circuits
,”
IEEE Trans. Circuits Syst., I
41
,
499
503
(
1994
).
39.
X.
Wang
and
M.
Wang
, “
A hyperchaos generated from Lorenz system
,”
Physica A
387
,
3751
3758
(
2008
).
40.
G. M.
Mahmoud
,
M. A.
Al-Kashif
, and
A. A.
Farghaly
, “
Chaotic and hyperchaotic attractors of a complex nonlinear system
,”
J. Phys. A: Math. Theor.
41
,
055104
(
2008
).
41.
Y. R.
Shen
,
The Principles of Nonlinear Optics
(
John Wiley & Sons
,
Hoboken
,
2003
).
42.
I.
Sliwa
,
P.
Szlachetka
, and
K.
Grygiel
, “
Generation of strongly chaotic beats
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
18
,
835
840
(
2008
).
43.
J.
Cartwright
,
D. L.
Gonzalez
, and
O.
Piro
, “
Nonlinear dynamics of the perceived pitch of complex sounds
,”
Phys. Rev. Lett.
82
,
5389
5392
(
1999
).
44.
E.
Bradley
and
H.
Kantz
, “
Nonlinear time-series analysis revisited
,”
Chaos
25
,
097610
(
2015
).

Supplementary Material

You do not currently have access to this content.